{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:MD5EWMYNE446JCB7XDE2L4B4TO","short_pith_number":"pith:MD5EWMYN","schema_version":"1.0","canonical_sha256":"60fa4b330d2739e4883fb8c9a5f03c9ba9f229608406a416ad3ed2ff7c9bb224","source":{"kind":"arxiv","id":"2308.12273","version":5},"attestation_state":"computed","paper":{"title":"Assouad-Nagata dimension of minor-closed metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.GR","math.GT","math.MG"],"primary_cat":"math.CO","authors_text":"Chun-Hung Liu","submitted_at":"2023-08-23T17:42:31Z","abstract_excerpt":"Assouad-Nagata dimension addresses both large and small scale behaviors of metric spaces and is a refinement of Gromov's asymptotic dimension. A metric space $M$ is a minor-closed metric if there exists an (edge-)weighted graph $G$ satisfying a fixed minor-closed property such that the underlying space of $M$ is the vertex-set of $G$, and the metric of $M$ is the distance function in $G$. Minor-closed metrics naturally arise when removing redundant edges of the underlying graphs by using edge-deletion and edge-contraction. In this paper, we determine the Assouad-Nagata dimension of every minor"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2308.12273","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-08-23T17:42:31Z","cross_cats_sorted":["cs.DM","math.GR","math.GT","math.MG"],"title_canon_sha256":"6230fa0d8055c3712c53b0f5017a2b8bf4d5747d4794dcda9361f20f012725c8","abstract_canon_sha256":"8e2aacf76c70ca777af60fc585bb0350f4c59085be66b2217d712b77532f30f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:34:05.145294Z","signature_b64":"RTRmujU44GAqCc+6Hpuq1Z24bSfo1IEByNHJWaFJjP7sV+BZU3gp+bYFV29ZsODgxQIpaTMajkJlfX7JoKHnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60fa4b330d2739e4883fb8c9a5f03c9ba9f229608406a416ad3ed2ff7c9bb224","last_reissued_at":"2026-07-05T10:34:05.144762Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:34:05.144762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Assouad-Nagata dimension of minor-closed metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.GR","math.GT","math.MG"],"primary_cat":"math.CO","authors_text":"Chun-Hung Liu","submitted_at":"2023-08-23T17:42:31Z","abstract_excerpt":"Assouad-Nagata dimension addresses both large and small scale behaviors of metric spaces and is a refinement of Gromov's asymptotic dimension. A metric space $M$ is a minor-closed metric if there exists an (edge-)weighted graph $G$ satisfying a fixed minor-closed property such that the underlying space of $M$ is the vertex-set of $G$, and the metric of $M$ is the distance function in $G$. Minor-closed metrics naturally arise when removing redundant edges of the underlying graphs by using edge-deletion and edge-contraction. In this paper, we determine the Assouad-Nagata dimension of every minor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.12273","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.12273/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2308.12273","created_at":"2026-07-05T10:34:05.144821+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.12273v5","created_at":"2026-07-05T10:34:05.144821+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.12273","created_at":"2026-07-05T10:34:05.144821+00:00"},{"alias_kind":"pith_short_12","alias_value":"MD5EWMYNE446","created_at":"2026-07-05T10:34:05.144821+00:00"},{"alias_kind":"pith_short_16","alias_value":"MD5EWMYNE446JCB7","created_at":"2026-07-05T10:34:05.144821+00:00"},{"alias_kind":"pith_short_8","alias_value":"MD5EWMYN","created_at":"2026-07-05T10:34:05.144821+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.10164","citing_title":"Quasi-isometries, contractions, and intersection graphs","ref_index":32,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO","json":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO.json","graph_json":"https://pith.science/api/pith-number/MD5EWMYNE446JCB7XDE2L4B4TO/graph.json","events_json":"https://pith.science/api/pith-number/MD5EWMYNE446JCB7XDE2L4B4TO/events.json","paper":"https://pith.science/paper/MD5EWMYN"},"agent_actions":{"view_html":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO","download_json":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO.json","view_paper":"https://pith.science/paper/MD5EWMYN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.12273&json=true","fetch_graph":"https://pith.science/api/pith-number/MD5EWMYNE446JCB7XDE2L4B4TO/graph.json","fetch_events":"https://pith.science/api/pith-number/MD5EWMYNE446JCB7XDE2L4B4TO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO/action/storage_attestation","attest_author":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO/action/author_attestation","sign_citation":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO/action/citation_signature","submit_replication":"https://pith.science/pith/MD5EWMYNE446JCB7XDE2L4B4TO/action/replication_record"}},"created_at":"2026-07-05T10:34:05.144821+00:00","updated_at":"2026-07-05T10:34:05.144821+00:00"}